Abstract

We introduce a closed-loop feedback technique to actively control the coupling condition of an optical cavity, by employing amplitude modulation of the interrogating laser. We show that active impedance matching of the cavity facilitates optimal shot-noise sensing performance in a cavity enhanced system, while its control error signal can be used for intra-cavity absorption or loss signal extraction. We present the first demonstration of this technique with a fiber ring cavity, and achieved shot-noise limited loss sensitivity. We also briefly discuss further use of impedance matching control as a tool for other applications.

© 2008 Optical Society of America

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  1. J. Ye, L.-S. Ma, and J. L. Hall, "Ultrasensitive detections in atomic and molecular physics: demonstration in molecular overtone spectroscopy," J. Opt. Soc. Am. B 15, 6-15 (1998).
    [CrossRef]
  2. W. Demtröder, Laser Spectroscopy, Basic Concepts and Instrumentation, 2nd Enlarged Ed., (Springer-Verlag, Germany, 2003).
  3. R. van Zee and J. Patrick Looney, eds., Cavity-Enhanced Spectroscopies:Experimental Methods in the Physical Sciences (Academic Press, California, USA, 2002) Vol. 40.
  4. T. McGarvey, A. Conjusteau, and H. Mabuchi, "Finesse and sensitivity gain in cavity-enhanced absorption spectroscopy of biomolecules in solution," Opt. Express 14, 10441-10451 (2006).
    [CrossRef] [PubMed]
  5. A. E. Siegman, Lasers (University Science, Mill Valley Calif., 1986).
  6. R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, "Laser phase and frequency stabilization using an optical resonator," Appl. Phys. B 31, 97-105 (1983).
    [CrossRef]
  7. J. H. Chow, M. B. Gray, I. C. M. Littler, and D. E. McClelland, "Spectroscopic detection system and method," Australian Patent Application No. 2007906639.
  8. P. R. Saulson, Fundamentals of Interferometric Gravitational Wave Detectors (World Scientific Publishers, Singapore, 1994).
    [CrossRef]
  9. M. Cai, O. Painter, and K. J. Vahala, "Observation of critical coupling in a fiber taper to a silica-microsphere whispering-gallery mode system," Phys. Rev. Lett. 85, 74-77 (2000).
    [CrossRef] [PubMed]
  10. D. S. Rabeling,  et. al., "Experimental demonstration of impedance matching locking and control for coupled resonators," manuscript under preparation.

2006

2000

M. Cai, O. Painter, and K. J. Vahala, "Observation of critical coupling in a fiber taper to a silica-microsphere whispering-gallery mode system," Phys. Rev. Lett. 85, 74-77 (2000).
[CrossRef] [PubMed]

1998

1983

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, "Laser phase and frequency stabilization using an optical resonator," Appl. Phys. B 31, 97-105 (1983).
[CrossRef]

Cai, M.

M. Cai, O. Painter, and K. J. Vahala, "Observation of critical coupling in a fiber taper to a silica-microsphere whispering-gallery mode system," Phys. Rev. Lett. 85, 74-77 (2000).
[CrossRef] [PubMed]

Conjusteau, A.

Drever, R. W. P.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, "Laser phase and frequency stabilization using an optical resonator," Appl. Phys. B 31, 97-105 (1983).
[CrossRef]

Ford, G. M.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, "Laser phase and frequency stabilization using an optical resonator," Appl. Phys. B 31, 97-105 (1983).
[CrossRef]

Hall, J. L.

J. Ye, L.-S. Ma, and J. L. Hall, "Ultrasensitive detections in atomic and molecular physics: demonstration in molecular overtone spectroscopy," J. Opt. Soc. Am. B 15, 6-15 (1998).
[CrossRef]

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, "Laser phase and frequency stabilization using an optical resonator," Appl. Phys. B 31, 97-105 (1983).
[CrossRef]

Hough, J.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, "Laser phase and frequency stabilization using an optical resonator," Appl. Phys. B 31, 97-105 (1983).
[CrossRef]

Kowalski, F. V.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, "Laser phase and frequency stabilization using an optical resonator," Appl. Phys. B 31, 97-105 (1983).
[CrossRef]

Ma, L.-S.

Mabuchi, H.

McGarvey, T.

Munley, A. J.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, "Laser phase and frequency stabilization using an optical resonator," Appl. Phys. B 31, 97-105 (1983).
[CrossRef]

Painter, O.

M. Cai, O. Painter, and K. J. Vahala, "Observation of critical coupling in a fiber taper to a silica-microsphere whispering-gallery mode system," Phys. Rev. Lett. 85, 74-77 (2000).
[CrossRef] [PubMed]

Rabeling, D. S.

D. S. Rabeling,  et. al., "Experimental demonstration of impedance matching locking and control for coupled resonators," manuscript under preparation.

Vahala, K. J.

M. Cai, O. Painter, and K. J. Vahala, "Observation of critical coupling in a fiber taper to a silica-microsphere whispering-gallery mode system," Phys. Rev. Lett. 85, 74-77 (2000).
[CrossRef] [PubMed]

Ward, H.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, "Laser phase and frequency stabilization using an optical resonator," Appl. Phys. B 31, 97-105 (1983).
[CrossRef]

Ye, J.

Appl. Phys. B

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, "Laser phase and frequency stabilization using an optical resonator," Appl. Phys. B 31, 97-105 (1983).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Express

Phys. Rev. Lett.

M. Cai, O. Painter, and K. J. Vahala, "Observation of critical coupling in a fiber taper to a silica-microsphere whispering-gallery mode system," Phys. Rev. Lett. 85, 74-77 (2000).
[CrossRef] [PubMed]

Other

D. S. Rabeling,  et. al., "Experimental demonstration of impedance matching locking and control for coupled resonators," manuscript under preparation.

J. H. Chow, M. B. Gray, I. C. M. Littler, and D. E. McClelland, "Spectroscopic detection system and method," Australian Patent Application No. 2007906639.

P. R. Saulson, Fundamentals of Interferometric Gravitational Wave Detectors (World Scientific Publishers, Singapore, 1994).
[CrossRef]

A. E. Siegman, Lasers (University Science, Mill Valley Calif., 1986).

W. Demtröder, Laser Spectroscopy, Basic Concepts and Instrumentation, 2nd Enlarged Ed., (Springer-Verlag, Germany, 2003).

R. van Zee and J. Patrick Looney, eds., Cavity-Enhanced Spectroscopies:Experimental Methods in the Physical Sciences (Academic Press, California, USA, 2002) Vol. 40.

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Figures (8)

Fig. 1.
Fig. 1.

Conceptual schematic of the CEAMLAS technique with a free space linear cavity. The reflectivity of the input coupler is variable via an actuation voltage. It is used to actively impedance match the cavity with a feedback control loop. The error signal for this control loop is provided by amplitude modulation of the laser and demodulation of the reflected light.

Fig. 2.
Fig. 2.

Theoretical minimum detectable shot-noise limited absorption vs. different cavity coupling conditions. The cavity coupling is varied by varying the input coupler reflectivity. The minimum shot-noise occurs when the cavity is impedance-matched, when r 1=r 2 e -αl . For this plot, we have assumed R 2=0.99; αl=1×10-4; β=0.01; η=1(A/W); and P opt=200 (µW)

Fig. 3.
Fig. 3.

The effect of increasing absorbing sample length on: a) the transmissivity of the input coupler to keep the cavity impedance-matched; b) the impedance-matched cavity finesse; and c) the theoretical minimum detectable shot-noise limited absorption coefficient.

Fig. 4.
Fig. 4.

The experimental schematic for the CEAMLAS demonstration. The fiber ring cavity has a variable input Coupler A for impedance-matching, while Coupler B introduces cavity loss to emulate intra-cavity absorption. The phase modulation and PDH frequency locking system ensure that the laser carrier is held on cavity resonance. The amplitude modulated carrier can then interrogate the impedance coupling condition of the cavity. The “error point” yields the open-loop cavity loss measurement while the “actuator point” yields the closed-loop cavity loss measurement.

Fig. 5.
Fig. 5.

(a) The optical power reflected off the fiber ring cavity as the laser frequency is scanned across resonance. (b) The PDH error signal that is used to lock the laser to resonance. This relies on 69MHz phase modulation sidebands. (c) the AM error signal used to measure cavity loss. The AM sidebands are at a frequency of 20MHz.

Fig. 6.
Fig. 6.

Experimental plots showing: (a) The fiber ring cavity output optical power while the ratio u of input Coupler A is scanned; (b) the corresponding cavity loss error signal recorded at the “error point” of Fig. 4. The coupling ratio for Coupler B was held constant at v 2=0.95.

Fig. 7.
Fig. 7.

(a) The AM error point voltage with a 1.5Hz loss signal injected into variable Coupler B of Fig. 4. (b) The corresponding fiber ring cavity output optical power.

Fig. 8.
Fig. 8.

A) FFT of the error point voltage; B) sum of shot noise and electronic noise; C) the electronic noise spectral density.

Equations (11)

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( α l ) SN = π 2 𝔉 × 2 e B η P opt
r res = r 1 r 2 e α l 1 r 1 r 2 e α l .
P opt = E 0 2 = A 2 .
E inc = A e i ω 0 t [ 1 + β 2 e + i ω m t + β 2 e i ω m t ] ,
E refl = A e i ω 0 t [ r 1 r 2 e α l 1 r 1 r 2 e α l + β 2 e + i ω m t + β 2 e i ω m t ] .
V sig η β P opt R pd r 1 r 2 e α l 1 r 1 r 2 e α l ,
Δ V sig η β P opt R pd [ r 2 e α l 1 r 1 r 2 e α l ( r 1 r 2 e α l ) ( r 1 r 2 e α l ) ( 1 r 1 r 2 e α l ) 2 ] Δ ( α l ) .
V SN = R pd e η P opt [ ( r 1 r 2 e α l 1 r 1 r 2 e α l ) 2 + β 2 2 ] ,
Δ ( α l ) min = ( 1 r 1 r 2 e α l ) 2 [ ( 1 r 1 r 2 e α l ) ( r 2 e α l ) ( r 1 r 2 e α l ) ( r 1 r 2 e α l ) ] β
  × e η P opt [ ( r 1 r 2 e α l 1 r 1 r 2 e α l . ) 2 + β 2 2 ] .
V sig η β P opt R pd Δ r 1 u v ,

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